On the recording, Mr. Bennett was in playful form, and when he pulled one of his signature surprises — a sudden change of key — Mr. Charlap responded without missing a beat. As he listened in the car, the pianist smiled as he recalled the ensemble class he had just finished teaching at Paterson, the first of the semester with this small group of students, which was also observed by a reporter. There, he had warned his students of the need to be prepared for sudden key changes.

“That was a perfect example of why you do your homework,” Mr. Charlap said as the CD played on.

Mr. Charlap practices what he preaches: At the end of the class in question, he asked the five students, who were instrumentalists, to memorize the words to “All the Things You Are.”

The unusual assignment is emblematic of what distinguished Mr. Charlap among the 80 jazz musicians and experts who applied for the director’s job when it opened up after the death of Mulgrew Miller in 2013, said David Demsey, the coordinator of jazz studies at Paterson and a member of the director’s search committee.

“Not only is he one of the world’s premier jazz pianists, but he is also one of the world’s foremost experts on the popular songbook,” Mr. Demsey said of Mr. Charlap.

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A colleague called Mr. Charlap "one of the world’s premier jazz pianists."CreditBryan Anselm for The New York Times

During Mr. Charlap’s ensemble class, it seemed that whether he was alone at the keyboard or in dynamic interplay with the students, he revealed a deep knowledge of both the process of songwriting and the way it can become a basis for improvisation.

He emphasized the wedding of lyrics to music as a key element in the “through-line” between the composers, the popular singers and the jazz artists who “all belong to each other” and are “all of a piece of the great fabric of this song.”

“The words drip off the notes,” he said. “The notes drip off the words.”

In one exchange, Mr. Charlap, who lives in West Orange, challenged Danny Raycraft, a senior from Fairport, N.Y., who plays alto saxophone, to consider the lyrics to the opening bars of “All the Things You Are” — “You are the promised kiss of springtime” — as he played.

After a few false starts, Mr. Raycraft added a subtle syncopation to his reading that observers agreed lent musical life to the lyrics. The process was repeated in one form or another throughout the class.

“I know those guys found something in ‘All the Things You Are’ they never heard before,” Mr. Demsey said.

Mr. Charlap said the students had begun to find the song’s larger meaning by connecting their interpretations with the intentions of its writers, Jerome Kern and Oscar Hammerstein. “If they can really learn to do that,” he said, “then the sky’s the limit for them hanging their own personality on it in a very real way, not in a way that dismisses history but in a way that embraces history.”

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Mr. Charlap teaches the importance of understanding the connection between lyrics and music, calling it a key element in learning improvisation.CreditBryan Anselm for The New York Times

Mr. Charlap, who will be 49 on Oct. 15, comes naturally to his approach. His father, Mark Charlap, known as Moose, was the Broadway composer who wrote the music to “Peter Pan.” And his mother, with whom he still performs, is the Grammy-nominated singer Sandy Stewart, who appeared with Perry Como on television variety shows in the 1950s and ’60s.

References to onetime cultural touchstones like “Peter Pan” and Perry Como, which Mr. Charlap used to introduce himself to his students on the first day of the ensemble class, did not seem to register. Nor did an allusion to sheet music, seeing that most young jazz musicians now use lead sheets called up on their cellphones. But Mr. Charlap was able to close the generational divide with his on-the-spot demonstration of how sheet music can guide musicians. Using alternating musical figures in his right and left hands, he created a hypothetical sheet-music version of “All the Things You Are” and then broke down the composition part by part, explaining how each part is equivalent to a section of an orchestra.

How Mr. Charlap’s pedigree, experience and teaching style will translate into shaping a jazz studies program will become clear over time, he said. Next year, Mr. Charlap will help curate the Jazz Room concert series. The 2015 season is the program’s 35th year, which will begin in the school’s Shea Center for the Performing Arts on Oct. 18 with the Italian pianist Rossano Sportiello. In April, Mr. Charlap will bring his trio to the series.

Mr. Charlap has chosen artists who represent the two sides of his musical personality — the popular composer Harold Arlen and the jazz pianist Horace Silver — as subjects for this semester’s Dialogue Days. For this curriculum requirement, participants will perform a work by Mr. Arlen or Mr. Silver and then be formally critiqued.

Students who attended his show at the Village Vanguard last month were already absorbing how Mr. Charlap likes to work. In his first set, he chose to perform standards like “Autumn in New York” and “I’ll Remember April.” But his interpretations of the tunes leaned toward the adventurous.

“He has the perfect combination,” Mr. Demsey said. “A gentle, kind nature. And he is a force.”